Warning: Technical article. If you are technically competent, then the following can be very useful for setting up different devices and avoiding lengthy map downloads.
OMN keeps its mapping in a series of pkg files in a defined directory structure. These will work on any device, but their access is controlled by your account, so if you don't have access to the map files, the account won't use them.
So lets take an easy example: You have downloaded all of your maps to your desktop PC, and you now wish to populate your laptop without re-downloading all of the map data.
1. Pop into Settings->My Account, and it will tell you where you map data is located, on a PC, this is most likely C:\ProgramData\Outdoor Map Navigator\pkgs
2. Pop into Settings->My Account on the laptop, and it will more than likely have the same directory. Tip, if its a new machine, download one demo map, as this will create the directory structure that you need to locate.
3. Using a usb drive / network connection (this is where you need to be technically competent), copy the files from the location we identified in point 1 to the location identified in point 2.
4. The data is now on the second machine, but its almost like in a corrupt state - as OMN didn't download it, it hasn't catalogued it and doesn't know about it. This is easy to rectify, please just follow the instructions on Repairing Map Data.
If you can locate the Source and Destination directories, and you can physically copy the map data, then the above will work on all platforms.
On Windows and macOS, things are fairly open and easy.
iOS is very locked down and I don't believe this is possible.
Android - it is possible, but again it can be complex due to how Android Storage works. (Again, this is where you need to be technically competent, and this isn't something we can offer support for as it differs hugely between devices.). First up, please see this link: Android SD Cards. Internal Storage is normally non-accessible by 3rd party tools. You will most likely need a Custom Path or External may work. What you need to do is, download the OMN software, download say one demo map and check you can view it. Then, and this is the hard bit, move it to a location that you can also access via a 3rd party tool, be that connecting it to your PC or other - i.e. a way that you are comfortable copying data to the Android device. If you can locate the directory where the demo map is, and you can copy in a test file, then you are pretty much on the right track - now just follow the process above to copy your files and catalogue the data.